1. Constant mode in meson correlators at finite temperature
Takashi Umeda
This talk is based on the hep-lat/
to appear in Phys. Rev. D
Tsukuba Theory Seminar, Univ. of Tsukuba, Apr. 20, 2007
Tsukuba Theory Seminar
T.Umeda (Tsukuba)

2. Contents Introduction - Overview - Search for Quark Gluon Plasma
- (Sequential) J/ψ suppression
Quenched QCD calculations
- Lattice setup
- T dependence of charmonium correlators
- Constant mode in meson correlators
Discussion & summary
Most of this talk is not so recent studies
Tsukuba Theory Seminar
T.Umeda (Tsukuba)

3. Quark Gluon Plasma (QGP)
from Munster Univ. web-site
Most of this talk is not so recent studies
Tsukuba Theory Seminar
T.Umeda (Tsukuba)

4. Experiments SPS : CERN ( – 2005) Super Proton Synchrotron
RHIC: BNL (2000 – now)
Relativistic Heavy Ion Collider
LHC : CERN ( )
Large Hadron Collider
Most of this talk is not so recent studies
from the Phoenix group web-site
Tsukuba Theory Seminar
T.Umeda (Tsukuba)

5. Signatures of QGP J/ψ suppression T.Hashimoto et al.,
PRL57 (1986) 2123.
T.Matsui & H.Satz,
PLB178 (1986) 416.
Most of this talk is not so recent studies
Talk by Heavy Ion Cafe
Tsukuba Theory Seminar
T.Umeda (Tsukuba)

6. First paper on the J/ψsuppression
photo : Prof. Osamu Miyamura
The preprint of this paper is cited by the Matsui&Satz paper.
Tsukuba Theory Seminar
T.Umeda (Tsukuba)

7. J/ψ suppression in Exp. Phys.Lett.B477(2000)28 NA50 Collaboration
Most of this talk is not so recent studies
Phys.Lett.B477(2000)28
NA50 Collaboration
QM2006
PHENIX Collaboration
Tsukuba Theory Seminar
T.Umeda (Tsukuba)

8. Spectral Function in lattice QCD
C(t) : meson correlator
Nt = 1/(aT)
T: temperature
Quenched QCD
- T. Umeda et al.,
EPJC39S1, 9, (2005).
- S. Datta et al.,
PRD69, , (2004).
- T. Hatsuda & M. Asakawa,
PRL92, , (2004).
- A. Jakovac et al.,
PRD75, (2007).
Full QCD
- G. Aarts et al.,
hep-lat/
Most of this talk is not so recent studies
In the studies of SPFs on the lattice,
all studies indicate survival of J/ψ state above Tc (1.5Tc?)
Tsukuba Theory Seminar
T.Umeda (Tsukuba)

9. Sequential J/ψsuppression
Particle Data Group (2006)
for the total yield of J/ψ
10%
30%
E705 Collaboration,
PRL70, 383, (1993).
60%
Most of this talk is not so recent studies Ps V S Av
Dissociation temperatures of J/ψ and ψ’& χc
are important for QGP phenomenology.
Tsukuba Theory Seminar
T.Umeda (Tsukuba)

10. χc states on the lattice
S. Datta et al.,
PRD69, (2004).
A.Jakovac et al.,
PRD75, (2007).
Most of this talk is not so recent studies
Tsukuba Theory Seminar
T.Umeda (Tsukuba)

11. Contents Introduction - Overview - Search for Quark Gluon Plasma
- (Sequential) J/ψ suppression
Quenched QCD calculations
- Lattice setup
- T dependence of charmonium correlators
- Constant mode in meson correlators
Discussion & summary
Most of this talk is not so recent studies
Tsukuba Theory Seminar
T.Umeda (Tsukuba)

12. Quenched QCD at T>0 Lattice setup anisotropic lattices : 203 x Nt
1/as = 2.03(1) GeV, as/at = 4
Clover quark action with tadpole imp. on anisotropic lattice
H. Matsufuru et al., PRD64, (2001).
rs=1 to reduce cutoff effects in higher energy states
F. Karsch et al., PRD68, (2003).
quark mass is tuned with MJ/ψ(= 3097MeV)
Most of this talk is not so recent studies
equilib. is 20K sweeps
each config. is separated
by 500 sweeps
Tsukuba Theory Seminar
T.Umeda (Tsukuba)

13. Effective mass (local mass)
Definition of effective mass
when
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In the (anti) periodic b.c.
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14. At zero temperature (our lattice results) MPS = 3033(19) MeV
MV = 3107(19) MeV
(exp. results from PDG06)
Mηc = 2980 MeV
MJ/ψ = 3097 MeV
Mχc0 = 3415 MeV
Mχc1 = 3511 MeV
Most of this talk is not so recent studies
In our lattice Nt ⋍ 28 at Tc
t = 1 – 14 is available near Tc
Spatially extended (smeared) op. is discussed later
Tsukuba Theory Seminar
T.Umeda (Tsukuba)

15. Quenched QCD at T>0 small change in S-wave states
 survival of J/ψ & ηc at T>Tc
drastic change in P-wave states
 dissociation of χc just above Tc (?)
Most of this talk is not so recent studies
S. Datta et al.,
PRD69, (2004). etc...
Tsukuba Theory Seminar
T.Umeda (Tsukuba)

16. Constant mode Now we consider the meson correlator with p=0 & mq1=mq2
exp(-mqt) x exp(-mqt)
= exp(-2mqt)
mq is quark mass
or single quark energy
exp(-mqt) x exp(-mq(Lt-t))
= exp(-mqLt)
Lt = temporal extent
in imaginary time formalism
Lt = 1/Temp.
gauge field : periodic b.c.
quark field : anti-periodic b.c.
in confined phase: mq is infinite
 the effect appears
only in deconfined phase
Most of this talk is not so recent studies
Pentaquark (KN state):
two pion state:
 Dirichlet b.c.
c.f. T.T.Takahashi et al.,
PRD71, (2005).
Tsukuba Theory Seminar
T.Umeda (Tsukuba)

17. Free quark calculations
for Ps, V, S and Av channels
163 x 32 isotropic lattice
Wilson quark action
with mqa = 0.2
Most of this talk is not so recent studies
Obvious constant contribution
in P-wave states
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T.Umeda (Tsukuba)

18. Free quark calculations
Continuum form of the correlators
calculated by S. Sasaki
Most of this talk is not so recent studies
where
: single quark energy with relative mom. p
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19. Spectral representation
Spectral function of the correlator
F. Karsch et al.,
PRD68, (2003).
G. Aarts et al.,
NPB726, 93 (2005).
with
Most of this talk is not so recent studies
chiral symmetry in massless limit
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20. Physical interpretation
constant contribution remains
in the continuum form & infinite volume
The constant term is related to some transport coefficients.
From Kubo-formula, for example, a derivative of the SPF
in the V channel is related to the electrical conductivity σ.
Most of this talk is not so recent studies
Tsukuba Theory Seminar
T.Umeda (Tsukuba)

21. Without constant mode How much does SPF change at the region
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from “An Introduction to Quantum Field Theory”
Michael E. Peskin, Perseus books (1995)
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T.Umeda (Tsukuba)

22. Midpoint subtraction An analysis to avoid the constant mode
Midpoint subtracted correlator
Free quarks
Free quarks
Most of this talk is not so recent studies
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23. Z3 symmetrization Here we consider the Z3 transformation Z3 symmetric
Z3 asymmetric
The asymmetry of diag-(b)
is coming from a factor of Re[exp(-i2πn/3)]
Most of this talk is not so recent studies
Z3 asym. terms are removed because
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T.Umeda (Tsukuba)

24. Averaged correlators
However, this is not an exact method to avoid the constant contribution.
Most of this talk is not so recent studies
The 3 times wrapping diagram
is also Z3 symmetric.
the contribution is not canceled.
but, O(exp(-mqNt)) » O(exp(-3mqNt))
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T.Umeda (Tsukuba)

25. Midpoint subtraction analysis
usual effective masses at T>0
subtracted effective mass
Most of this talk is not so recent studies
0.1at=800MeV
the drastic change in P-wave states disappears in meffsub(t)
 the change is due to the constant mode
Tsukuba Theory Seminar
T.Umeda (Tsukuba)

26. Polyakov loop sector dependence
after Z3 transformation
const.  Re(exp(-i2πn/3))*const.
even below Tc, small const. effect
enhances the stat. fluctuation.
drastic change in P-states disappears.
Results for Av channel
Most of this talk is not so recent studies
Tsukuba Theory Seminar
T.Umeda (Tsukuba)

27. Results with extended op.
Spatially extended operators:
with a smearing func. φ(x)
in Coulomb gauge
point source func.
smeared source func.
Most of this talk is not so recent studies
The extended op. yields large overlap with lowest states
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T.Umeda (Tsukuba)

28. Results with extended op.
usual effective mass
subtracted effective mass
averaged effective mass
Most of this talk is not so recent studies
extended op. enhances
overlap with const. mode
small constant effect
is visible in V channel
no large change above Tc
in meffsub(t) and meffave(t)
Tsukuba Theory Seminar
T.Umeda (Tsukuba)

29. Discussion point operators extended operators subtracted averaged
The drastic change of P-wave states is due to the const. contribution.
 There are small changes in SPFs ( except for ω=0 ).
Why several MEM studies show the dissociation of χc states ?
Most of this talk is not so recent studies
Tsukuba Theory Seminar
T.Umeda (Tsukuba)

30. Difficulties on non-lowest states
M(J/ψ(1S)) = 3097MeV
M(ψ(2S)) = 3686MeV
MEM test using T=0 data
# data
for T/Tc=0
for T/Tc=0.6
for T/Tc=1.2
Most of this talk is not so recent studies
T. Hatsuda & M. Asakawa,
PRL92, (2004).
It is difficult to reproduce the non-lowest states peak at T>0
Furthermore P-wave states have larger noise than S-wave states
English is strange ….
Tsukuba Theory Seminar
T.Umeda (Tsukuba)

31. Discussion Most systematic & reliable calc.
using MEM for charmonium SPFs
They have concluded that
the results of SPFs for P-states
are not so reliable.
e.g. large default model dep.
the drastic change just above Tc
is reliable results.
Most of this talk is not so recent studies
A.Jakovac et al., hep-lat/
Tsukuba Theory Seminar
T.Umeda (Tsukuba)

32. Conclusion
There is the constant mode in charmonium correlators above Tc
The drastic change in χc states is due to the constant mode
 the survival of χc states above Tc, at least T=1.4Tc.
The result may affect the scenario of J/ψ suppression.
In the MEM analysis,
one has to check consistency of the results at
using, e.g., midpoint subtracted correlators.
Most of this talk is not so recent studies
Tsukuba Theory Seminar
T.Umeda (Tsukuba)

33. Discussion Several groups have presented
almost no change in Ps channel
small but visible change
in V channel
Most of this talk is not so recent studies
These results can be explained
by the constant contribution.
- no constant in Ps channel
- small constant in V channel
(proportional to pi2)
in free quark case
H. Iida et al., PRD74, (2006).
Tsukuba Theory Seminar
T.Umeda (Tsukuba)

34. Discussion H. Iida et al., PRD74, 074502 (2006).
Most of this talk is not so recent studies
S-wave states : PBC p=( 0, 0, 0 ) < xAPBC p=( π/L, 0, 0 )
P-wave states : PBC p=( 2π/L, 0, 0 ) > xAPBC p=( π/L, 0, 0 )
P-const : PBC p=( 0, 0, 0 ) < xAPBC p=( π/L, 0, 0 )
Tsukuba Theory Seminar
T.Umeda (Tsukuba)

35. Discussion Polyakov loop sector dependence S. Chandrasekharan et al.,
Most of this talk is not so recent studies
S. Chandrasekharan et al.,
PRL82, 2463, (1999).
Tsukuba Theory Seminar
T.Umeda (Tsukuba)

36. Volume dependence
Size of the constant contribution depends on the volume Ns3
The dependence is negligible at Ns/Nt ≳ 2
Results on 963 x 32
( Ns/Nt=3  similar to T>0 quench QCD calculation )
Most of this talk is not so recent studies
Tsukuba Theory Seminar
T.Umeda (Tsukuba)